I do not understand the worry. Just carry. If you are not supposed to be carrying in an area you will have someone mention it, but probably not. Go on with your life and stop worrying about your weapon. When you get nervous about it, others pick up on that.
Just carry.
Rest stops are owned by the state. You are fine carrying at them. I have done so without issues.
http://www.wsdot.wa.gov/Safety/RestAreas/rules.htm
I actually thought this was a good question and one I never thought about. As far as I know as many others have said they are run by the state no worries there but I still thought it was a good question to ask. Thanks for getting my mind working this morning
Just be sure you don't "splash" anything on your firearm while at the urinal and all will be OK.
For some WA State Rest Areas it's a good idea to be carrying. Some are pretty remote with some strange critters hanging out at them.